| dc.description.abstract | The continuing scaling of VLSI technology and the increase of design complexity have rendered the robustness of analog circuits a significant design concern. Analog circuits with strong parasitic effects can be modeled using a multi-loop structure, which is more sophisticated than the traditional single feedback loop structure and results in a more complex small signal stability analysis from the noise perspective. A Loop Finder algorithm has been proposed to allow designers to detect and identify noise-sensitive return loops, which are also called "unstable" loops in previous works, without the need to add breakpoints in the circuit. Besides, efficient pole discovery and impedance computation methods have been explored so that the Loop Finder algorithm can deal with very large scale analog circuits in a reasonable amount of time. However, this algorithm only works for circuits that can be described using a linear time-invariant (LTI) system model. Many practical circuits, such as switch capacitor filters, mixers and so on, have time-varying behaviors. To describe such circuits, a linear time-varying (LTV) system model needs to be employed.
In this research, we first examine the stability property of LTV systems in time domain, mostly based upon the Floquet Theory. We then take an in-depth look at the transfer function of an LTV system in the frequency domain and build the link between it and the Floquet theory. Finally, we propose an efficient algorithm for identifying noise-sensitive loops in linear time-varying circuits. This methodology provides a unifying solution for loop-based noise analysis for both LTI and LTV circuits. | en |
